Problem: In Takahashi's mind, there is always an integer sequence of length 2 \times 10^9 + 1: A = (A_{-10^9}, A_{-10^9 + 1}, ..., A_{10^9 - 1}, A_{10^9}) and an integer P.

Initially, all the elements in the sequence A in Takahashi's mind are 0, and the value of the integer P is 0.

When Takahashi eats symbols `+`, `-`, `>` and `<`, the sequence A and the integer P will change as follows:

* When he eats `+`, the value of A_P increases by 1;
* When he eats `-`, the value of A_P decreases by 1;
* When he eats `>`, the value of P increases by 1;
* When he eats `<`, the value of P decreases by 1.



Takahashi has a string S of length N. Each character in S is one of the symbols `+`, `-`, `>` and `<`. He chose a pair of integers (i, j) such that 1 \leq i \leq j \leq N and ate the symbols that are the i-th, (i+1)-th, ..., j-th characters in S, in this order. We heard that, after he finished eating, the sequence A became the same as if he had eaten all the symbols in S from first to last. How many such possible pairs (i, j) are there?

Constraints

* 1 \leq N \leq 250000
* |S| = N
* Each character in S is `+`, `-`, `>` or `<`.

Input

Input is given from Standard Input in the following format:


N
S


Output

Print the answer.

Examples

Input

5
+>+<-


Output

3


Input

5
+>+-<


Output

5


Input

48
-+><<><><><>>>+-<<>->>><<><<-+<>><+<<>+><-+->><<


Output

475

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

typedef unsigned long long ULL;

const int MAXN = 2.5e5 + 10;
const ULL P = 233ULL, iP = 7204522363551799129ULL;

int n;
ULL hsh1[MAXN], hsh2[MAXN];
char s[MAXN];
std::map <ULL, int> mp;

int main() {
	scanf("%d %s", &n, s + 1), hsh2[0] = 1;
	for (int i = 1; i <= n; ++i) {
		hsh1[i] = hsh1[i - 1], hsh2[i] = hsh2[i - 1];
		if (s[i] == '+') hsh1[i] += hsh2[i];
		else if (s[i] == '-') hsh1[i] -= hsh2[i];
		else if (s[i] == '<') hsh2[i] *= iP;
		else hsh2[i] *= P;
		++mp[hsh1[i]];
	}
	ULL ans = 0;
	for (int i = 1; i <= n; ++i) ans += mp[hsh1[n] * hsh2[i - 1] + hsh1[i - 1]], --mp[hsh1[i]];
	printf("%llu\n", ans);
	return 0;
}